Exam 4: Mechanical Objects, Part 2
Suppose you have two identical particles that attract each other with a certain gravitational force. Now you move them so they are three times as far apart as they were originally, but the force between them stays the same. What is one way in which the masses might change so the force could remain constant?
Since the separation is being tripled the force would go to 1/9 its original value if the masses remained constant. Therefore the product of the masses must increase by a factor of 9 to make up for the distance change. This could be done in many ways. One mass could increase by 9 times, both masses could increase by 3 times, one mass could reduce to 1/3 its original value and the other could increase to 27 times its original value, etc. If we require the masses to remain identical then for both masses must increase by a factor of 3.
Consider astronauts orbiting the earth in the space shuttle.
-Suppose that the astronauts are traveling at a speed of 1000 m/sec. What must the radius of their circular orbit be if their acceleration is 8.5 m/sec2?
Here we can use a = v2/r. 8.5 = (1000)2/r
8.5 = 106/r
r = 106/8.5 = 1.18x105 m
You are substitute teaching for your spouse and are using balloons to demonstrate how rockets work. The balloons are blown up and released so that the air can leave them rapidly. Why do the balloons fly all around, even though the balloon does not have a surface to push against?
The balloons start to move because of momentum transfer. The initial momentum of the balloon with air in it before release is zero. Then when the balloon is opened, air rushes out of it. Since the total momentum of the air and balloon is still zero, the balloon recoils in the opposite direction and therefore moves forward. In a sense, the balloon is pushing against its own air that it is releasing.
Suppose you have two identical particles that attract each other with a certain gravitational force. Now you move them so they are one quarter as far apart as they were originally, but the force between them stays the same. What is one way in which the masses might change so the force could remain constant?
What is the gravitational force that two 100 kg persons exert on each other when standing 1m apart?
The relativistic momentum of a 1000 kg car moving at 0.95 times the speed of light is
Consider the Moon orbiting the Earth. _______ is the centripetal force for the orbit, and one could therefore measure the mass of the ________ by studying the Moon's orbit.
The relativistic energy of a 1000 kg car moving at 0.95 times the speed of light is
When sitting still on the ground, a tricycle is in a state of
Suppose you are spending your weekend on roller skates trying to get momentum from somewhere. Which of the following will give you momentum in the north direction?
At various times in the news it has been reported that certain vehicles are susceptible to rolling over. The physical mechanism that is responsible for rollovers is
Ideal physics theory would tell you that, if you climb into a basket at a store you cannot go from one side of the store to the other. In fact you can do this, and physicists often take breaks from late night test writing to do such things. Please explain why ideally we should not be able to do this but in reality we can.
The speed at which a car must move so that its relativistic momentum is twice its nonrelativistic momentum is
What is one advantage and one drawback of a very large wheel on a bicycle or tricycle whose operator can pedal the front wheel?
The speed at which a car must move so that its relativistic energy is three times its rest energy is
Consider astronauts orbiting the earth in the space shuttle.
-The acceleration of gravity in the orbiting space shuttle is over 90% that on the surface of the earth but the astronauts still feel weightless (no apparent weight) please explain. You may assume the orbit is perfectly circular.
Please explain why tricycles are better at sitting still than bicycles are, but bikes are the vehicles of choice when you want to be moving.
What are three drawbacks to a bicycle or tricycle whose front wheel can be pedaled?
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